How to get vertex normals from a shape-key in Python?
The only way I can think of is to use Object.to_mesh() and read normals from this temp mesh datablock, before freeing it (see also the doc):

me = my_ob.to_mesh(scene, True, 'Render', False, False)
for v in me.vertices:
    print(v.normal)
bpy.data.meshes.remove(me)


Quite obviously, you need to set the influence of your shape key accordingly first.